Blind Source Separation with Outliers in Transformed Domains

Blind source separation (BSS) methods are well suited for the analysis of multichannel data. In many applications, the observations are corrupted by an additional structured noise, which hinders most of the standard BSS techniques. In this article, we propose a novel robust BSS approach able to jointly unmix the sources and separate the source contribution from the structured noise or outliers. It first builds on a new sparse component modeling that allows combining both the spectral and morphological/spatial diversity of the sources and the outliers. We introduce the tr-rGMCA algorithm (robust generalized morphological component analysis in transform domains) to tackle the underlying robust BSS problem. Numerical experiments highlight the robustness and precision of the proposed method in a wide variety of settings, including the full-rank regime.